Question: Simplify the following expression: $ k = -1 - \dfrac{7r + 1}{r + 6} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{r + 6}{r + 6}$ $ \dfrac{-1}{1} \times \dfrac{r + 6}{r + 6} = \dfrac{-r - 6}{r + 6} $ Therefore $ k = \dfrac{-r - 6}{r + 6} - \dfrac{7r + 1}{r + 6} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{-r - 6 - (7r + 1) }{r + 6} $ Distribute the negative sign: $k = \dfrac{-r - 6 - 7r - 1}{r + 6}$ $k = \dfrac{-8r - 7}{r + 6}$